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Abstract: Analytical investigation of the free vibration behavior of thin circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material based on the classical plate theory (CPT) is presented in this paper. The material properties of the FG substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from three-dimensional finite element analyses. [Copyright &y& Elsevier]

This article investigates the nonlinear vibration behavior of multiscale nanocomposites nanoshell subjected to hygrothermal environment and resting on elastic foundations. The novelty and contribution of this article is considering a multiscale doubly curved sandwich nanoshell. Three-phase composite nanoshell composes of polymer-Carbon nanotube-fiber (PCF) and polymer-Graphene platelet-fiber (PGF) according to Halpin-Tsai model. Various distributions patterns such as U (uniform), X, A and O are considered. The classical shell theory and nonlocal strain gradient theory including von Kármán strain–displacement relationships are employed to build the size-dependent governing equations. The governing equations of multiscale nanoshell have been implemented by Hamilton's principle and solved by homotopy perturbation method. For investigating correctness and accuracy, this paper is validated by other previous researches. Finally, the effects of different parameters such as temperature rise, various distributions patterns and curvature ratio have been investigated. • Nonlinear vibration behavior of multiscale nanocomposites nanoshell is investigated in hygrothermal environment. • The influence of different parameters such as temperature rise, various distributions patterns, curvature ratio are investigated in detail. • Various distributions patterns such as U (uniform), X, A and O are considered. • Via the classical shell theory and the von Kármán type hypothesis the displacements are expressed. • Nonlocal strain gradient governing equations of multiscale nanoshell have been implemented by employing the Hamilton's principle. • Using the homotopy perturbation method, the equations of motions are solved. • The governing equations of multiscale shell have been derived by implementing Hamilton's principle. [ABSTRACT FROM AUTHOR]

This is the first research on the free vibration analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic annular plate resting on the visco-Pasternak foundation and subjected to the nonlinear temperature gradient and mechanical loading within the framework of higher-order shear deformation theory (HSDT). Hamilton's principle is employed to establish governing equations within the framework of HSDT. In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Generalized differential quadrature method (GDQM) is applied to obtain a numerical solution. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of the stiffness of the substrate, patterns of temperature rise, axial load, damper and viscoelasticity coefficient, weight fraction and distribution patterns of GPLs and geometric dimensions of GPLs on the frequency response of the structure. The results revealed that applying sinusoidal temperature rise and locating more square-shaped GPLs in the vicinity of the top and bottom surfaces have important effect of the highest natural frequency and buckling load of the FG-GPLRC viscoelastic structure. • Free vibration analysis of FG-GPLRC viscoelastic annular plate is investigated. • The effects of the nonlinear temperature gradient and mechanical load is considered. • Hamilton's principle is employed to establish governing equations of motion within the framework of HSDT. • Viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. • The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. [ABSTRACT FROM AUTHOR]